Bell, who is in his first year as the Pirates hitting coach, played for the D-backs from 1998-2002, and he served as Bob Melvin's bench coach there in 2005 and '06.
When Bell left his position following the 2006 season to spend more time with his family, the team hired Gibson to replace him.
Gibson got plenty familiar with Bell, as Bell served as a special instructor for the team during Spring Training and was hitting coach for Arizona's Double-A affiliate in Mobile last year.
"Just the length guys stay on the ball," Gibson said when asked what about the Pirates' approach made him see Bell's influence. "I saw guys choking up. I know how Jay believes. I know what Jay's end goal is with it, and I just think they'll probably start to buy in on some of it."
Bell played for the Pirates for eight years, and he said it was one of only a few places he would have considered leaving the D-backs' organization for.
"This has been a great opportunity over here," Bell said. "It's back in a place that I'm extremely familiar with. The fans know who I am. I know a lot of people in the front office still from the days that I was here. This is a great opportunity to get back to the big leagues."